The paper provides a theoretical framework for analyzing policy formation among independent authorities operating in an interdependent environment. This is then applied to the analysis of optimal monetary policy in a stochastic two-country model with rational expectations. The main conclusions are 1) Optimal monetary policy requires a finite response of the money supply to the exchange rate (which is the only contemporaneously observed variable.) Neither a fixed nor a freely floating exchange rate is likely to be optimal. 2) Output stabilizing monetary policy may well require 'leaning with the wind' in the foreign exchange market, expanding the money supply when the home currency depreciates, thus increasing the volatility of the exchange rate. 3) The ability of the monetary authorities to influence real variables is due to the assumption that the private sector does not make exchange rate-contingent forward contracts.4) There are likely to be gains from policy coordination.